Welcome to the new Becker-Posner Blog, maintained by the University of Chicago Law School.

03/19/2006

The Cost of the War in Iraq--Posner's Comment

One of the major questions that I asked in my book Catastrophe: Risk and Response (Oxford University Press, 2004) is what can be salvaged of cost-benefit analysis in situations of enormous uncertainty. I think a lot, and refer the reader of this blog to chapter 3 of my book for explanation. The war in Iraq (not discussed in my book) provides a test case for this proposition.
Apparently the Administration did not conduct a cost-benefit analysis before deciding for war. Maybe it thought the benefits so obviously great that no reasonable estimate of cost would exceed them. I believe that the Administration's only public estimate was that the war would cost no more than $60 billion and that some of this expense would be defrayed (as in the 1991 war with Iraq) by other countries. The estimate seems to have assumed that the probability of a short, cheap (i.e., $60 billion maximum), victorious war was 1.
A responsible cost-benefit analysis would have costed alternative scenarios (such as short-victorious war, long-victorious war, long-losing war, and long-breakeven war), attached a probability or, more plausibly, a range of probabilities to each, and summed the expected costs generated by multiplying each cost estimate by its associated probability or range of probabilities. Benefits to be valued would include (1) elimination of Iraq's weapons of mass destruction, (2) a demonstration of U.S. military prowess that would intimidate hostile nations such as Iran and North Korea, (3) cost savings from eliminating the containment regime (the no-fly zones and sanctions enforcement designed to box in Saddam Hussein), and (4) improvement in our military capabilities as a result of wartime experience. (1), (3), and (4) seem susceptible of quantification, though (1) would have been overestimated by virtually everyone because of the widespread and highly plausible, but erroneous, belief that Iraq had an active WMD program. (2) could probably be ignored on the ground that it was likely to be offset by adverse reactions to our embracing a doctrine of preventive war. I would have given no weight to the Wolfowitz project of promoting democracy in the Arab region, as it is completely uncertain whether democracy in that region is in the interests of the United States. We have certainly not been pleased with the result of the democratic election in Palestine that has brought Hamas to power. We would not like to see the Muslim Brotherhood take power in Egypt, though it may be the most popular political group there. We were distinctly displeased with the result of the Iranian presidential election.
I would also ignore the effect of the Iraq war on our struggle against international terrorism. I imagine the effect is negative, but there is too much uncertainty to try to quantify it.
In a paper first published in March 2003, very shortly before the war began, the economists Steven Davis, Kevin Murphy, and Robert Topel conducted a limited cost-benefit analysis. It was basically just a comparison between the cost of going to war and the cost of continuing the containment policy. They estimated the former as $125 billion maximum and the latter as between $380 billion and $630 billion. The gravest weakness of their analysis was the failure to consider war alternatives to the short, cheap, victorious war that the Administration assumed. They recently updated their paper and raised their estimate of the cost of the war to $323 billion, while allowing (no doubt chastened by their original underestimate) for the possibility that it might go higher. This seems too low since the budgetary cost of the war is already $250 billion and increasing at the rate of $6 billion a month. The costs can of course be capped at any time by U.S. withdrawal from Iraq, but then the benefits of the war would have to be written down to zero except for the important and curiously ignored benefit that consists of having one‚Äôs armed forces engaged in a recent war. The lessons of war cannot be duplicated by peacetime training, planning, and analysis.
Linda Bilmes and Joseph Stiglitz in a recent paper estimate the cost of the Iraq war as being between $1 trillion and $1.2 trillion. As Becker points out, the estimate is based in part on entirely speculative estimates concerning the impact of the war on the price of oil. My own view, moreover, is that higher oil prices are a very good thing from the standpoint of combating global warming, though I would prefer to see them brought about by high taxes on fossil fuels, which would have the additional benefit of reducing the wealth of oil-producing nations. The Bilmes and Stiglitz paper usefully emphasizes, however, the costs resulting from the unexpectedly long deployments of our troops. Apparently, as they point out, these were not anticipated and thus impounded in military salaries and benefits, and as a result the nation is having to incur increased recruitment and other personnel costs in order to maintain the armed forces at the desired level. With the dubious (as Becker notes) cost items subtracted from the Bilmes-Stiglitz estimate, the total is still a sizable $840 billion, which as Becker points out approaches the high end of the Davis-Murphy-Topel current estimate.
I have two disagreements with Becker. First, I do not think that a comparison of U.S. military deaths in Iraq and Vietnam is meaningful. Partly because of increased media coverage, there is much greater sensitivity to casualties today than there was in the Vietnam era (or think back to the Civil War--twice as many deaths as in World War II, in a population less than one-fourth as large). Apparently the Administration has decided that it is imperative to reduce the number of U.S. military deaths in Iraq, even though the total for 2005 was only 846, compared to 14,000 in 1968, the critical year of the Vietnam war.
Second, I would not count the welfare of Iraqis in a cost-benefit analysis of U.S. warmaking. I do not think most Americans want to sacrifice American lives and resources for the sake of foreigners. There is some American altruism toward Iraqis, and to that extent increasing the welfare of Iraqis is a benefit to Americans, but, in my view, only to that extent. And I think it is quite slight.
All this said, I do not think a decision to go to war should be based on cost-benefit analysis. It would terrify the world if powerful nations conducted cost-benefit analyses of whether to go to war. There are 192 nations besides the United States; should we ask the Defense Department to advise us which ones we should invade because the expected benefits would exceed the expected costs? Might a conquest of Canada produce net benefits for the United States? Rather, our policy should be to wage only defensive wars, though that would include aiding allies that have been attacked, which was a reasonable basis for our entry into the Vietnam war, though the results were deeply disappointing.
I also do not think a nation threatened with attack should base a decision whether to defend or surrender on cost-benefit analysis. Rather, it should commit itself to fight regardless, as such a commitment will in most instances greatly increase the expected cost of the attack. That is the economic logic of revenge and the basis of our policy of massive retaliation during the Cold War.
I said that the Administration did not conduct a cost-benefit analysis of the war in Iraq, and I have also said that I do not think a decision to go to war should be based on such an analysis. But in the case of a war that though in a broad sense defensive is also optional because there is no immediate threat of attack by the enemy, cost-benefit analysis has an important role to play. After 9/11, the danger to be anticipated from Saddam Hussein's possessing weapons of mass destruction, though uncertain, had to be reckoned greater than before. And by virtue of the no-fly zones and the sanctions, the United States was already in a quasi-war with Iraq. Against the background, the decision of the Administration to obtain a United National resolution demanding that Iraq re-admit the inspectors whom it had ousted in 1998 was reasonable and had the support of most nations. Enforcing the demand required the United States to station large forces in Kuwait and elsewhere in attack range of Iraq. In March 2003 the United States had the choice of permitting Saddam's cat-and-mouse game with the inspectors to continue, or invading. That was the point at which a careful cost-benefit analysis might have indicated the desirability of holding off on invading for a month or two, although a significant cost would have been that it would have given Saddam more time to prepare and that having to fight in hot months would have impeded the invasion to a degree.
In addition, once the decision for war was taken, cost-benefit analysis of alternative scenarios--in particular of the possibility of a long war that we would lose or draw--might have indicated net benefits from committing more troops to the invasion and its immediate aftermath in order to prevent the rise of an insurgency.

TrackBack

Comments

You can follow this conversation by subscribing to the comment feed for this post.

One mathematical and one rhetorical quibble. First, the mathematical.

A responsible cost-benefit analysis would have costed alternative scenarios (such as short-victorious war, long-victorious war, long-losing war, and long-breakeven war), attached a probability or, more plausibly, a range of probabilities to each, and summed the expected costs generated by multiplying each cost estimate by its associated probability or range of probabilities.

I am not sure it is meaningful to specify a range of probabilities instead of a single probability, at least not in a single cost-benefit analysis. Since the range of probabilities must itself be given a weight distribution in order to carry out the cost-benefit analysis, the mean of that distribution might as well be the assigned probability of the scenario. E.g., if the probability of a scenario is "in the range of 5%-15%," with each point in the range being implicitly given uniform weight, then in a linear cost-benefit analysis, the result will be the same as for a scenario with an assigned probability of 10%. Then the "range" seems merely obfuscatory.

But there may be other operations, e.g. combining disparate probability estimates from several analysts, in which it makes sense to speak of probabilities-of-probabilities.

Also:
After 9/11, the danger to be anticipated from Saddam Hussein's possessing weapons of mass destruction, though uncertain, had to be reckoned greater than before.

Although this view is commonly expressed, I do not see the logic of it. Eight years prior to 9/11, terrorists tried to destroy the World Trade Center with a car bomb. On 9/11, terrorists successfully destroyed the World Trade Center with hijacked planes. The first event might have alerted us to the existence of terrorists. Why would the second event increase the reckoned danger of Iraqi weapons of mass destruction?

One might argue with greater logic that 9/11 showed that (a) the terrorists had not acquired any weapons of mass destruction, since they did not use them; and (b) the terrorists did not necessarily require weapons of mass destruction, as that term is normally used, to kill large numbers of people.

I think there were other options than just war or containment. For example, the US could have bombed Iraq or expanded the sanction regime. A proper cost-benefit analysis would have accounted for these as well.

"First, I do not think that a comparison of U.S. military deaths in Iraq and Vietnam is meaningful. Partly because of increased media coverage, there is much greater sensitivity to casualties today than there was in the Vietnam era (or think back to the Civil War--twice as many deaths as in World War II, in a population less than one-fourth as large)."

The media coverage is an interesting part of this. Politicians may have an incentive to minimize short-term costs even if it means maximizing total or long-term costs.

So, for example: suppose the U.S. could have gotten a lot of terrorists and ended things in Tora Bora but at a very high cost of human life in a very short time period. This may have cost elected politicians in the U.S. an election win even though it may have kept long-term terrorist costs low. I am not sure on this.

Thus, politicans may have incentives to let things dribble along over many years in a fashion that is, cumulatively, very expensive - and more expensive than taking a one-time, big-bath and cleaning things up quickly.

People in organizations are not always rewarded for being up-front about difficult issues and fixing them.

All this said, I do not think a decision to go to war should be based on cost-benefit analysis. It would terrify the world if powerful nations conducted cost-benefit analyses of whether to go to war.This is an excellent point.A big part of the problem here is that one group of people (the USA) is doing a cost benefit analysis of a course of action where it is primarily someone else (the Iraqis) who are bearing the costs.If people in the United States had to decide what percentage of long term increase in GDP would "justify" an invasion and occupation of the United States, the percentage would be much higher than the percentage increase in GDP that would "justify" invasion and occupation of Iraq.People in the United States were motivated to spend huge amounts on security after a couple buildings were destroyed on 9/11. This suggests that the percentage increase in GDP necessary for people in the United States to want to be invaded (and likely have entire cities destroyed) would have to be astronomical.Society does not allow murder on the basis of whether there is economic benefit to the murderer. Society does not allow slavery on the basis of whether there is economic benefit to the slave owner. The international community does not allow war on the basis of whether there is economic benefit to the invader.

Benefits to be valued would include (1) elimination of Iraq's weapons of mass destruction, ... (1) would have been overestimated by virtually everyone because of the widespread and highly plausible, but erroneous, belief that Iraq had an active WMD program.It is unlikely that anyone (even the Bush administration) believed, at the time of invasion, that Iraq had the capability to launch a major attack on the United States.If the Bush administration had believed for example, that Iraq had nuclear weapons and the capability to deliver them to the United States, they would not have invaded. In fact, if Iraq had had nuclear weapons at all at the time of invasion it is unlikely that the Bush administration would have invaded. Furthermore, the UN weapons inspectors were clear that Iraq did not have nuclear weapons.Even if Iraq had merely had the capability to launch a major attack on the United States using chemical or biological weapons it is unlikely that the United States would have invaded. Despite Colin Powell pulling that ridiculous stunt at the UN holding up a test tube of white powder and implying that it could kill millions if it was smashed on a sidewalk somewhere, none of the chemical or biological weapons that Iraq could possibly have had were significantly more capable of causing destruction than the conventional weapons that Iraq was known to (and allowed to) have.It would have been easier and more effective for Iraq to sneak a few dozen tanks into Manhattan and use them to shell buildings and machine gun pedestrians than to try to sneak truckloads of poisons gas into the USA and then try to create a poison gas cloud that drifted over all of Manhattan at just the right concentration to be lethal.

Observation: the war, seen in the wake of 9/11, now seems less about literal dangers to the US (WMD, connections between Al Queda and Hussein, regime change, etc.) and more about transforming the region by force and, through the expected "stability" such a decision would engender, making the region and the US safer such that a second 9/11 becomes much less likely. Given this premise, could a cost/benefit analysis ever been successfully applied to such an endeavor? After all, if the Bush policy in Iraq works, an interesting thing ultimately comes about as a result: nothing. By that I mean, when you are successful in defending the nation from terrorist attack, nothing, i.e., no 9/11-type event, occurs. This makes it harder, if not impossible, to quantify whether the endeavor has been worth it because people quite naturally want to see something result as the "bang" for their heavily-taxed "buck"--not to mention the tragedy of American blood being shed. And without that something, the politicians have a hard sell (witness Bush's low poll numbers). Bush's PR problem concerning the war is that he is taking hundreds of billions in tax dollars to provide what the public perceives it already has--peace and quiet. In conclusion, we know the approximate "cost" side of the analysis, but how does one figure nothing into the "benefit" side of the analysis?

Social choices as to war frequently don't make overall cost-benefit sense retrospectively as considered in an open society. Witness the Civil War. But, except with omniscience & other divine attributes, there may be no "overall sense," only our more or less informed, though not necessarily correct, conjectures as to possble outcomes. There may also be differences in social networks making it likely that some will not survive. Moreover, that contingency might be one for which human beings, or its decisive sets in a populations, were selected.
One reason for war is seeming myopia. Witness the Civil War. But if the social-capital network* is sufficiently depleted by expansion of another group's social capital, what looks like myopia & an ill-considered spasm response might instead be characterized as an implicit calculation that war would shorten the conflict, lower the long-term cost, and avert replacement of the social network. Then some seeming myopia might have survival value. The next couple of elections may determine the applicability of that contingency and for whom in the present conflict.
* On which see Prof. Becker's "Preferences and Tastes" in Accounting for Tastes.

The "economic logic of revenge"- Cold War style- is only effective if it results in deterrence, and it only deters if there are nukes on both sides, and mutually assured destruction is the ultimate risk. This is my only quibble with Posner, with whom I otherwise agree.

The usefulness of cost-benefit analysis of war is limited to its assessment of costs. As Posner points out by his reference to the Palestinian election of Hamas, it is not now clear that "democracy" in the Middle East is a benefit to the United States. Also note Iranian election of conservatives. Ridding the world of a dictator like Hussein can only be valued as far as the American altruism which Posner correctly identifies as minimal at best. Finally, the discovery of WMDs being the only legitimate purpose, having found none, we would have realized the largest benefit of this war, and incurred NONE of the subsequent costs of occupation and democratization.

War? What war? It was over in less than three months. What we're fighting now is the Peace, which is much more difficult to win. If I remember correctly, we're still under a cease-fire mode on the DMZ of the 38th Parallel in Korea. Peace is tough battle to fight. How many years have we been there?

Just one question, how did we ever get down this road? We were advised years ago, "to stay out of the Bloody affairs of Europe." Somehow the tables have turned and it's Europe that's trying to stay out of the "Bloody affairs of America."
Peace? we got a long road ahead of us. Unless we cut and run.

I think a socially-useful cost-benefit analysis of the Iraq war is made especially difficult by the fact that it is (relatively) easy to determine its approximate costs, but much more difficult to estimate the possible benefits.

How does one put a number on the value of the benefit to Iraq and the world of having a democracy in Iraq instead of a dictatorship? Over (e.g.) 50 years?

What is the value of the benefit of 300 million Arabs moving from Salafist or Ba'athist dictatorships to free-market, liberal democracies -- over 50 years?

Yet these are the stated goals of the war.

I would defer to Professors Becker & Posner on this, but my guess is that it would be at least an order of magnitude more difficult to rationally estimate the magnitude of these benefits -- there are so many unknowns and unknowables.

Practically speaking, we are thus ultimately left with decision-making on the basis of an idealistic belief in the universal value of free-market and liberal-democratic institutions -- or a cynical disbelief in the same.

Sun Tzu (the original and ultimate game strategist) said that effective war is waged at the enemyís expense. He also said that it is unwise to attack unless swift and decisive victory is assured--and that long, expensive and bloody struggles are NOT the product of well thought out strategies. Even if we do eventually win the war in Iraq, it will still be a fiasco for us economically.

However, I could be wrong. Perhaps the real strategy is Machiavellian. Perhaps Bush and company believe that it is not wise policy to let the rabble (US citizens) have too much money. Too much money means too much freedom and a consequent risk of (in Machiavelliís mind) instabilityóand we canít have that. What would become of the social order if citizens could solve their own problems without government taxes on their backs?

Ayn Rand once said that if socialism wins, it wonít be due as much to the efforts of leftist agitators as to that of right wing cronyism. All economic systems are ultimately based on trustóor they die.

Judge Posner's analysis is invariably fascinating, if not always convincing.

My question here would be, what is the probability that decision-makers antecendently committed by ideology to some general approach to war and foreign policy--whether it be "neoconservative," "realist," or "liberal-internationalist"--could be induced to change their opinion by some cost-benefit assessment, however constructed? Unless we can assign a probability to that, the recommendation to pay more attention to cost-benefit calculations is merely another ideology in competition with those already in the field.

Why isn't the debate over costs and benefits here simply another form of moral preaching?

I think a socially-useful cost-benefit analysis of the Iraq war is made especially difficult by the fact that it is (relatively) easy to determine its approximate costs, but much more difficult to estimate the possible benefits.The same could be said about a wide variety of crimes. For example, there are lot of mean stupid people in the world and it is likely that a rigorous cost-benefit analysis would find a net benefit in their death. That has not, however, lead society to conclude that it is OK to commit murder if, in the murderer's opinion, there will be a net benefit in the victims death.How does one put a number on the value of the benefit to Iraq and the world of having a democracy in Iraq instead of a dictatorship? Over (e.g.) 50 years?Given that Saddam Hussein is almost seventy, it is unlikely that he would have been an effective dictator for more than another decade or so. It is entirely possible that had Saddam remained in power Iraq would have undergone a gradual transistion to democracy on a time scale of a few decades. In that case, the relevant comparison would be a decade of brutal occupation followed by a gradual transition to democracy versus a decade of brtual dictatorship followed by a gradual transition to democracy.At any rate, if the Bush administration's assertion's about the unpopularity of Saddam's regime have any truth at all, then it is highly unlikely that Saddam's government would have been able to maintain power for fifty years.

OT: if one wanted to, say, print out posts from the Becker-Posner blog and read them on the bus, they would be disappointed as this blog's posts don't print well. To be specific: posts on this blog only print one page when printed normall and the rest of the text is cut off... here's an example:

Here are a couple factors not yet mentioned that would also seem to be critical, yet difficult to quantify:

(1) The current generation of U.S. military is getting some serious, hard-core battle experience, and involving essentially a terrorist/counterinsurgency network mode of asymmetrical warfare, and learing from it daily. That is a huge benefit. (I'll pick the battle-hardened military over the one that has been sitting around or even just drilling without conflict any day, wouldn't you?). But in terms of the value of this military preparedness, how do you quantify that economically?

(2) By coming in closer and direct contact with the enemy, in a theater from whence a good chunk of them come, you can gain a much more accurate evaluation of the import and impact of their threats, their strategy, resources, etc. which is essential for our crafting a more "global" response to the Islamist threat. I recall watching one of the 9/11 documentaries in which one of the first military responder planes that went up had the outdated approach of, "is it the Russians?" In other words, the military now has a far better understanding of who the enemy is, where they are coming from, etc. That in and of itself makes us safer than if the military was still stuck in the more myopic Cold War model.

(3) Our pre-war intelligence is plainly abysmal. I've read the good judge's book re the 9/11 commission and the supposed improvements made to our intelligence bureauacrazies (no, not a typo) and it was utterly discouraging. To the extent we have a footprint in the area, and can cultivate intelligence resources via native Arabic/Farsi speakers, a friendly Iraqi government, etc., we will be vastly better off because yes, then the next nuclear attack (or even the location of the Iranian reactors, etc.) may become known, and less intrusive steps taken to stop the problem at the outset, rather than have US cities destroyed. Again though, not easy stuff to monetarily quantify.

You wrote, "I would not count the welfare of Iraqis in a cost-benefit analysis of U.S. warmaking. I do not think most Americans want to sacrifice American lives and resources for the sake of foreigners."

Considering that the administration now justifies the war, in large part, on precisely this basis - i.e., that it is helping Iraq and Iraqis (and has the United States ever gone to war without saying this was a large part of its motivation?), I don't think we can simply ignore the welfare of Iraqis in our cost-benefit analysis. In short, since the US presumes to be doing what it's doing in Iraq's interest, it would be hypocritical to set aside Iraqi interests in evaluating cost/benefit.

"(1) The current generation of U.S. military is getting some serious, hard-core battle experience, and involving essentially a terrorist/counterinsurgency network mode of asymmetrical warfare, and learing from it daily. That is a huge benefit."

I am not sure they (US military) are getting the type of experience that is relevant. We are fighting a foe who set up decentralized cells around the world - not a traditional or guerilla army in a foreign land. This is an intelligence and economic war as much as a traditional or guerilla war. So some of the experience may be valuable and transferable, but not as much as some might think.

The U.S. govt (fed and local) in the U.S. was improvable during Katrina, including law enforcement and role of military. It did not look like lessons from Iraq helped.

We should be blogging about economic security and emergency response in the U.S.

"It is entirely possible that had Saddam remained in power Iraq would have undergone a gradual transition to democracy on a time scale of a few decades." -- Wes at March 21, 2006 07:07 PM

Possible, but highly unlikely.

More likely Saddam's sons would maintain an increasingly brutal regime until the entire Iraqi social structure was so rotten that it collapsed into complete anarchy, which spilled over into every neighboring country in the region.

Considering the importance of the region, one can estimate that likelihood and the costs of that only by saying "unacceptably high" and "astronomically high".

When it comes to intelligence, a good trustworty operative on the ground is worth thousands of eyes in space (opp's I let the secret out on that). But then, that ain't hi-tech nor costs millions of tax dollars. Something the Washington Bureauracy hasn't quite figured out yet. As it stands, I'm suprised we don't have more failures than we do.

More likely Saddam's sons would maintain an increasingly brutal regime...There are two possible scenarios for how Saddam could have transferred power to his sons: either while he was alive or after his death. The first scenario is not all that likely because Saddam didn't trust his sons but if it occurred there is a good chance Saddam could have made the transition successful. The second scenario is more likely but in that case it is less likely that the transition to a rule by his sons would be successful. I would estimate that the combined probability of a successful transfer of control of Iraq to one of Saddam's son's is about 50 per cent....until the entire Iraqi social structure was so rotten that it collapsed into complete anarchy,...This is possible but a collapse into complete anarchy (as opposed to something like a military coup a couple decades down the road) would be unusual based on analysis of power transitions in other countries. I would estimate that the probability of complete anarchy resulting from the rule of Saddam's sons would be about 50 per cent....which spilled over into every neighboring country in the region.While it is possible that anarchy in Iraq could trigger a regional war, I see little reason to conclude that anarchy in Iraq would somehow be "contagious" to other neighboring countries. I would put the probability of anarchy spilling over into every neighboring country at less than 10 per cent.The cumulative probability that Iraq would come to be governet by Saddam Hussien's sons and disolve into anarchy which would spill over into every neighboring country is, therefore, by my estimate 50 percent of 50 percent of 10 per cent or 2.5 percent.Considering the importance of the region,...Other than providing an opportunity for the various religions of the world to engage in a pissing contest and providing a natural resource that is going to be depleted in a few decades anyway, I fail to see how this region is actually all that important. I mean, if energy is so important why isn't the Bush administration spending hundreds of billions on alternative energy research (even just getting nuclear energy going)?

I saw two very bold and important comments by Posner: (1) the decision whether to go to war should not be based on cost-benefit analysis and (2) support for a fossil fuel tax to encourage development of alternative energy sources. These ideas deserve more "airplay" and discussion in Washington power circles.

I wouldn't mind if a country decided not to start a war because the costs to that country outweighed the benefits. It strikes me as totally unethical, however, for a country to go to war solely because the benefits to itself outweigh the costs to itself.More broadly, where are the Americans who just want a government that is content to do the routine tasks of governmets (collect taxes and provide basic infrastructure - roads, police and a legal system, basic access to education, a defensive military, etc.)? Why do so many Americans seem to want their government to go off on some fool ideological crusade to dominate the world militarily?Personally, I don't much care whether I pay slightly higher taxes and get slightly better roads or pay slightly lower taxes and get slightly worse roads but, in my view, a government that goes off and try to lord it over the rest of the world militarily is totally and completely unacceptable.